please help with the following problem using the substitution method
y=2x
x+y=12
thanks
x + 2x = 12
3x = 12
x = 4
y = 2x = 8
To solve this problem using the substitution method, follow these steps:
Step 1: Solve one equation for one variable.
In this case, we can solve the first equation for y:
y = 2x
Step 2: Substitute the expression for the variable into the other equation.
Now we substitute the expression for y (2x) into the second equation:
x + (2x) = 12
Step 3: Solve the resulting equation for the remaining variable.
Combine like terms:
3x = 12
Step 4: Solve for x.
Divide both sides of the equation by 3:
x = 4
Step 5: Substitute the value of x back into one of the original equations to solve for y.
Using the first equation, substitute x = 4:
y = 2(4)
y = 8
Therefore, the solution to the system of equations is x = 4 and y = 8.